Search any question & find its solution
Question:
Answered & Verified by Expert
If $y=\log \left[a^{3 x}\left(\frac{5-x}{x+4}\right)^{\frac{3}{4}}\right]$, then $\frac{d y}{d x}=$
Options:
Solution:
2509 Upvotes
Verified Answer
The correct answer is:
$3 \log a-\frac{3}{4(5-x)}-\frac{3}{4(x+4)}$
$y=\log \left[a^{3 x}\left(\frac{5-x}{x+4}\right)^{\frac{3}{4}}\right]$
$\begin{aligned} \therefore y &=\log _{a} 3 x+\log \left(\frac{5-x}{x+4}\right)^{\frac{3}{4}} \\ &=3 x \log a+\frac{3}{4} \log (5-x)-\frac{3}{4} \log (x+4) \end{aligned}$
$\therefore \frac{d y}{d x}=3 \log a+\frac{3(-1)}{4(5-x)}-\frac{3}{4(x+4)}$
$=3 \log a-\frac{3}{4(5-x)}-\frac{3}{4(x+4)}$
$\begin{aligned} \therefore y &=\log _{a} 3 x+\log \left(\frac{5-x}{x+4}\right)^{\frac{3}{4}} \\ &=3 x \log a+\frac{3}{4} \log (5-x)-\frac{3}{4} \log (x+4) \end{aligned}$
$\therefore \frac{d y}{d x}=3 \log a+\frac{3(-1)}{4(5-x)}-\frac{3}{4(x+4)}$
$=3 \log a-\frac{3}{4(5-x)}-\frac{3}{4(x+4)}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.